Search

The main objective of this paper is to introduce the concept of a Geraghty's cyclic contraction which is a generalized cyclic contractive mapping and provide best proximity point theorems for such a mapping in complete metric space and uniformly convex Banach space. Moreover, we also give some examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the modified proximal point algorithm for common fixed points of asymptotically quasi-nonexpansive mappings in CAT(0) spaces and also prove some convergence theorems of the proposed algorithm to a common fixed point of asymptotically quasi-nonexpansive mappings and a minimizer of a convex function. The main results in this paper improve and generalize the corresponding results given by some authors. Moreover, we then give numerical examples to illustrate and show efficiency of the proposed algorithm for supporting our main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the best proximity point theorem for α-proximal contraction of the first and second kinds in Banach spaces by using fixed point theorems. Also, we mention an example for justification of our results. [ABSTRACT FROM AUTHOR]

In this article, recognizing the innovative concept of complex valued fuzzy set due to Ramot et al. [1], we introduce the notion of complex valued fuzzy metric spaces. Several allied topological aspects for complex valued fuzzy metric spaces are also defined which fortify the concept. Moreover the complex valued fuzzy version of some celebrated and essential results from metric spaces including Banach contraction principle and the main theorem of Jungck [2] are established. Additionally some fixed point theorems satisfying certain rational expressions are proved. [ABSTRACT FROM AUTHOR]

We introduce the notion of a modified α- ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]

In this paper, we prove common coupled fixed point theorems under a Geraghty-type condition using monotone instead of the often used mixed monotone property. Also we give some sufficient conditions for the uniqueness of a common coupled fixed point. An example illustrating our results is provided. [ABSTRACT FROM AUTHOR]

In this paper, we consider the KKM maps defined for a nonself map and the correlated intersection theorems in Hadamard manifolds. We also study some applications of the intersection results. Our outputs improved the results of Raj and Somasundaram [17, V. Sankar Raj and S. Somasundaram, KKM-type theorems for best proximity points, Appl. Math. Lett., 25(3):496-499, 2012.]. [ABSTRACT FROM AUTHOR]

The object of this paper is to extend the concept of β-admissible for multivalued mappings due to Mohammadi et al. [B. Mohammadi, S. Rezapour and N. Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory and Applications 2013 (2013), 24] to fuzzy mappings and utilize this concept to prove a common α-fuzzy fixed point theorem for a pair of fuzzy mappings. We also give illustrative example which demonstrate the validity of the hypotheses of our results. Some related results to common fixed point for multivalued mappings are also derived from the main result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general iterative process for approximating common fixed point of two nonexpansive mappings in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. Our results improve and extend the corresponding results of many others form Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]

We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors. [ABSTRACT FROM AUTHOR]

In this article, we define a tangential property which can be used not only for single-valued mappings but also for multi-valued mappings, and used it in the prove for the existence of a common fixed point theorems of Gregus type for four mappings satisfying a strict general contractive condition of integral type in metric spaces. Our theorems generalize and unify main results of Pathak and Shahzad (Bull. Belg. Math. Soc. Simon Stevin 16, 277-288, 2009) and several known fixed point results. [ABSTRACT FROM AUTHOR]

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others. [ABSTRACT FROM AUTHOR]

We introduce a new modified Ishikawa iterative process and a new W-mapping for computing fixed points of an infinite family of strict pseudo contractions mapping in the framework of q-uniformly smooth Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions. The results obtained in this paper extend and improve the recent results of Cai and Hu 2010, Dong et al. 2010, Katchang and Kumam 2011 and many others in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of monotone α -nonexpansive mappings in an ordered Banach space E with the partial order ≤, which contains monotone nonexpansive mappings as special case. With the help of the Mann iteration, we show some existence theorems of fixed points of monotone α -nonexpansive mappings in uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of the Mann iteration for finding an order fixed point of monotone α -nonexpansive mappings under the condition lim sup n → ∞ β n ( 1 − β n ) > 0 or lim inf n → ∞ β n ( 1 − β n ) > 0 . [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solution of a mixed equilibrium problem and the set of solution of the variational inequality problems for a relaxed (u,v)-cocoercive and µ-Lipschitz continuous mapping in Hilbert spaces. We show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions. Our results improve and extend the recent ones announced by [Y.J. Cho, X.Q. Qin, M. Kang, Some results for equilibrium problems and fixed point problems in Hilbert spaces, J. Comput. Anal. Appl. 11(2009) 294-316] and many others. [ABSTRACT FROM AUTHOR]