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On Huang and Noor's Open Problem [article]

Faik Gursoy
2015 arXiv   pre-print
In this paper, we introduce and analyze a new iterative algorithm for solving a class of variational inclusions involving H-monotone operators. The strong convergence of this algorithm is proved and estimate of its convergence rate is supplied as an answer to an open question posed by Huang and Noor [Huang, Z., Noor, M. A. (2007). Equivalency of convergence between one-step iteration algorithm and two-step iteration algorithm of variational inclusions for H-monotone mappings. Computers & Mathematics with Applications, 53(10), 1567-1571.].
arXiv:1501.03318v1 fatcat:6cw6ili2ufacnorhcepvdao3q4

Comparison of The Speed of Convergence Among Various Iterative Schemes [article]

Vatan Karakaya, Faik Gürsoy, Müzeyyen Ertürk
2014 arXiv   pre-print
We show that iterative scheme due to Karahan and \"Ozdemir (2013) can be used to approximate fixed point of contraction mappings. Furthermore, we prove that CR iterative scheme converges faster than the iterative scheme due to Karahan and \"Ozdemir (2013) for the class contraction mappings. Finally, we prove a data dependence result for contraction mappings by employing iterative scheme due to Karahan and \"Ozdemir (2013).
arXiv:1402.6080v1 fatcat:kk3p6lngi5bblcadkufuvuwvpu

λ-statistical convergent function sequences in intuitionistic fuzzy normed spaces [article]

Vatan Karakaya, Necip Şimşek, Müzeyyen Ertürk, Faik Gürsoy
2011 arXiv   pre-print
Fuzzy logic was introduced by Zadeh in 1965. Since then, the importance of fuzzy logic has come increasingly to the present.There are many applications of fuzzy logic in the field of science and engineering, e.g. population dynamics (Barros), chaos control (Feng,Fradkov), computer programming (Giles), nonlinear dynamical systems (Hong), etc. The concept of intuitionistic fuzzy set, as a generalization of fuzzy logic, was introduced by Atanassov in 1986. Quite recently Park has introduced the
more » ... cept of intuitionistic fuzzy metric space, and Saadati and Park studied the notion of intuitionistic fuzzy normed space. Intuitionistic fuzzy analogues of many concept in classical analysis was studied by many authors (Mursaleen, Rsaadati, Jebril, Dinda, etc.). The concept of statistical convergence was introduced by Fast. Mursaleen defined λ-statistical convergence in Muhammed. Also the concept of statistical convergence was studied in intuitionistic fuzzy normed space in Karakus..Quite recently, Karakaya et al. defined and studied statistical convergence of function sequences in intuitionistic fuzzy normed spaces. Mohiuddine and Lohani defined and studied λ-statistical convergence in intuitionistic fuzzy normed spaces (Lohani). In this paper, we shall study concept λ-statistical convergence for function sequences and investigate some basic properties related to the concept in intuitionistic fuzzy normed space.
arXiv:1112.3328v1 fatcat:mamzz5gvobhhxa27b7mivztfji

Existence and data dependence results for the fixed points of multivalued mappings [article]

Emirhan Hacıoğlu, Faik Gürsoy
2021 arXiv   pre-print
We introduce multivalued Górnicki mapping and various new types of multivalued enriched contractive mappings, viz., multivalued enriched Kannan mapping, multivalued enriched Chatterjea mapping, and multivalued enriched Cirić-Reich-Rus mapping. Then we establish some existence results for the fixed points of these multivalued contractive type mappings using the fixed point property of the average operator of the mappings. Furthermore, we present some data dependence results for the fixed points of mentioned classes of mappings.
arXiv:2108.06811v1 fatcat:3ohssuoxtffe5povis5ovmnm6q

A Picard-S Iterative Scheme for Approximating Fixed Point of Weak-Contraction Mappings [article]

Faik Gürsoy
2014 arXiv   pre-print
If {a n } ∞ n=0 converges faster than {b n } ∞ n=0 , then {u n } ∞ n=0 converges faster than {v n } ∞ n=0 to p. 4 Faik GÜRSOY Definition 3 [4] Let (B, · ) be a Banach space.  ...  1 n (1 − δ) 1 − a 2 n (1 − δ) x n − q n (26) + 1 − a 0 n (1 − δ) 1 − a 1 n 1 − a 2 n (1 − L) + a 1 n a 2 n δL x n − T x n + 1 − a 0 n (1 − δ) a 1 n L z n − T z n + 1 − a 0 n (1 − L) y n − T y n . 6 Faik  ... 
arXiv:1404.0241v1 fatcat:3kihedyvsjct5amhkc5ri5stzy

Bazı sabit nokta yineleme yöntemlerinin yakınsama davranışlarının incelenmesi

Faik Gürsoy
2017 Sakarya University Journal of Science  
ÖZ Bazı sabit nokta yineleme yöntemlerinin, belirli bir büzülme şartını sağlayan operatörlerin sınıfından seçilen elemanların karakterlerine bağlı olarak farklı yakınsama davranışları sergiledikleri nümerik bir örnek verilerek gösterilecektir. Anahtar Kelimeler: konveks ve hiperbolik metrik uzaylar, yakınsaklık, yineleme metotları Investigation of convergency behaviors of some fixed point iteration methods ABSTRACT It will be shown by providing a numerical example that some fixed point
more » ... methods exhibit different convergency behaviors depending on the characters of the members chosen from a class of operators satisfying a certain contractive condition. *
doi:10.16984/saufenbilder.278071 fatcat:cz7mkbhgmvg33dr3xm7o7vkyqm

Split variational inclusions for Bregman multivalued maximal monotone operators

Mujahid Abbas, Faik Gürsoy, Yusuf Ibrahim, Abdul Rahim Khan
2020 Reserche operationelle  
We introduce a new algorithm to approximate a solution of split variational inclusion problems of multivalued maximal monotone operators in uniformly convex and uniformly smooth Banach spaces under the Bregman distance. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. As application, we solve a split minimization problem and provide a numerical example to support better findings of our result.
doi:10.1051/ro/2020085 fatcat:wrclab54k5f65gykxyxkvfxoo4

A Picard-S iterative method for approximating fixed point of weak-contraction mappings

Faik Gürsoy
2016 Filomat  
Recently, Gürsoy and Karakaya [7] introduced a Picard-S iterative scheme as follows:                x 0 ∈ D, x n+1 = Ty n , y n = 1 − a 1 n Tx n + a 1 n Tz n , z n = 1 − a 2 n x n + a  ... 
doi:10.2298/fil1610829g fatcat:56dgsudtt5alrjer3yk6v6qhpm

Applications of Normal S-Iterative Method to a Nonlinear Integral Equation

Faik Gürsoy
2014 The Scientific World Journal  
It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.
doi:10.1155/2014/943127 pmid:25184158 pmcid:PMC4144309 fatcat:ifi5z7vfzjb5pmkc3p24g7w7ji

Characteristics of Pellet Injuries to the Orbit

A. Şahap Kükner, Turgut Yilmaz, Serdal Çelebi, Şafak Karslioğlu, Gürsoy Alagöz, Didem Serin, M. Akif Acar, M. Faik Özveren
2009 Ophthalmologica  
Purpose: To investigate the features of orbital injuries by pellets fired from the front. Design: Retrospective, 4 cases of pellet injuries. Methods: Five orbits of 4 patients who sustained pellet injuries received from the front were reviewed retrospectively. The course of injury and results were assessed. Radiological examinations were reviewed. The patients were evaluated between December 1996 and June 2004. Results: Five orbits of 4 patients sustained injuries caused by pellets fired from
more » ... anterior direction. The globe in the injured orbit was intact in 2 cases. Severe loss of vision was also present in these 2 globes due to optic nerve involvement. Final visual acuity was down to no light perception in 4 eyes and limited to light perception in 1 eye. Conclusions: The prognosis of orbital pellet injuries is, unfortunately, poor. A pellet passing through the floor of the orbit often causes double perforation of the globe and, once in the orbital aperture, it travels towards the apex as a result of the conical shape of the orbit and lodges in the optic canal or its entrance, severely damaging the optic nerve. Surgery or other treatments are usually unsuccessful. Even if the globe is intact, vision is usually severely impaired.
doi:10.1159/000228715 pmid:19609090 fatcat:y5brknggtbhxnfsqwx4cmnijfy

Stability and data dependence results for the Jungck--Khan iterative scheme

Abdul Rahim KHAN, Faik GÜRSOY, Vivek KUMAR
2016 Turkish Journal of Mathematics  
doi:10.3906/mat-1503-1 fatcat:3roki477hzeuffx7w5j655uxj4

Familial Tetra-Amelia Syndrome

Fatma Eskicioglu, Burcu Artunç Ülkümen, Halil Gürsoy Pala, Faik Mümtaz Koyuncu
2014 International Journal of Women s Health and Reproduction Sciences  
Tetra-amelia is known as an anomaly characterized by the absence of all four limbs. It is a rare congenital anomaly, with an incidence of 1.5-4 per 100,000 births. It occurs as a result of developmental interruption between 24th and 36th days after fertilization. Its etiology is not well known. It may be observed isolated or associated with other anomalies. In this paper, we present an interesting case of an intra-uterine diagnosed tetra-amelia male fetus with the recurrence in the previous two
more » ... more male fetuses in the same family. Tetraamelia syndrome observed in all three male fetuses of a couple with blood relationship is presented. The first two male newborn died just after birth due to prematurity in 28th and 32nd weeks. The third male fetus was in 23nd weeks of the intrauterine life. There was no exposure to teratogenic agents in this pregnancy. It detected that the third male baby had subcutaneous edema, intra-abdominal ascites and lateral ventricle enlargement in cranium. Since tetra-amelia due to genetic inheritance based on X chromosome was suspected, the family was offered the options of termination of pregnancy, karyotype analysis and genetic consultation.
doi:10.15296/ijwhr.2014.40 fatcat:jcaxyoceevhnditd3e2q5qjnha

Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

Vatan Karakaya, Necip Şimşek, Müzeyyen Ertürk, Faik Gürsoy
2012 Abstract and Applied Analysis  
The purpose of this work is to investigate types of convergence of sequences of functions in intuitionistic fuzzy normed spaces and some properties related with these concepts.
doi:10.1155/2012/157467 fatcat:bavtquj7mvdrziqcgrh4gk6yyq

Controllability and accumulation of errors arising in a general iteration method

Faik GÜRSOY, Abdul Rahim KHAN, Kadri DOĞAN
2021 Fundamental Journal of Mathematics and Applications  
In this paper, we propose and analyze a three-step general iteration method which is a special case of an iteration method proposed in (S. Thianwan and S. Suantai, Convergence criteria of a new three-step iteration with errors for nonexpansive nonself-mappings, Comput. Math. Appl. 52 (2006Appl. 52 ( ), 1107Appl. 52 ( -1118)). Here we intend to study directly the accumulation, estimation and control of random errors in the newly proposed general iteration method. We give conditions under which
more » ... e accumulated-error in our iteration method is bounded and controllable in a permissible range.
doi:10.33401/fujma.812274 fatcat:j6yprgmqdrbt5c4umzoclmfir4

Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

Vivek Kumar, Nawab Hussain, Abdul Khan, Faik Gürsoy
2020 Filomat  
Using different technique and weaker restrictions on parameters, convergence and stability results of an SP iterative algorithm with errors for a strongly accretive Lipschitzian operator on a Banach space are established. Validity of new convergence results is verified through numerical examples and convergence comparison of various iterative algorithms is depicted. As applications of our convergence result, we solve a nonlinear operator equation and a variational inclusion problem. Our results
more » ... are refinement and generalization of many classical results.
doi:10.2298/fil2011689k fatcat:b3yhy4337rgnng7k6xv2gwl7l4
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