Naseer Shahzad

Some results on fixed points of α-ψ-Ciric generalized multifunctions

In 2012, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave some results on a fixed point of the mappings (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012). In fact, their technique generalized some ordered fixed point results (see (Alikhani et al. in Filomat, 2012, to appear) and (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012)). By using the main idea of (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012), we give some new results for α-ψ-Ciric generalized multifunctions and some related self-maps. Also, we give an affirmative answer to a recent open problem which was raised by Haghi, Rezapour and Shahzad in 2012.

Fixed point theory for cyclic generalized contractions in partial metric spaces

In this article, we give some fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces.

On fixed points of α-ψ-contractive multifunctions

Recently Samet, Vetro and Vetro introduced the notion of α-ψ-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce the notion of α∗-ψ-contractive multifunctions and give a fixed point result for these multifunctions. We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.

Fixed Point Theory in Distance Spaces

Preface.- Part 1. Metric Spaces.- Introduction.- Caristis Theorem and Extensions.- Nonexpansive Mappings and Zermelos Theorem.- Hyperconvex metric spaces.- Ultrametric spaces.- Part 2. Length Spaces and Geodesic Spaces.- Busemann spaces and hyperbolic spaces.- Length spaces and local contractions.- The G-spaces of Busemann.- CAT(0) Spaces.- Ptolemaic Spaces.- R-trees (metric trees).- Part 3. Beyond Metric Spaces.- b-Metric Spaces.- Generalized Metric Spaces.- Partial Metric Spaces.- Diversities.- Bibliography.- Index.

Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings

In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.

Strong convergence of a proximal point algorithm with general errors

In this paper we construct a proximal point algorithm for maximal monotone operators with appropriate regularization parameters. We obtain the strong convergence of the proposed algorithm, which affirmatively answer the open question put forth by Boikanyo and Morosanu (Optim Lett 4:635–641, 2010).

Some notes on fixed points of quasi-contraction maps

In this paper, we shall give some results about fixed points of quasi-contraction maps on cone metric spaces. These results generalize some recent results.

Random fixed points of random multivalued operators on polish spaces

RANDOM coincidence point theorems and random fixed point theorems are stochastic generalizations of classical coincidence point theorems and classical fixed point theorems. Random fixed point theorems for contraction mappings in Polish spaces were proved by Spacek [l] and Hans (2, 31. For a complete survey, we refer to Bharucha-Reid [4]. Itoh [5] proved several random fixed point theorems and gave their applications to random differential equations in Banach spaces. Recently, Sehgal and Singh [7], Papageorgiou [8] and Lin [9] have proved different stochastic versions of the well-known Schauder’s fixed point theorem. The aim of this paper is to prove various stochastic versions of Banach type fixed point theorems for multivalued operators. Section 2 is aimed at clarifying the terminology to be used and recalling basic definitions and facts. Section 3 deals with random coincidence point theorems for a pair of compatible random multivalued operators. The structure of common random fixed points of these operators is also studied. In Section 4, the existence of a common random fixed point of two random multivalued operators satisfying the Meir-Keeler type condition in Polish spaces is proved. Section 5 contains a random fixed point theorem for a pair of locally contractive random multivalued operators in .s-chainable Polish spaces. As an application, a theorem on random approximation is also obtained.

Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps

The aim of this paper is to prove strong convergence of a modified implicit iteration process to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings. An immediate corollary of our theorems provides an affirmative response to a question raised by Xu and Ori [H.K. Xu, R. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].

Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an -multimap or a multimap such that both and are closed and have the KKM property for each Kakutani multimap . As applications, we obtain existence theorems of equilibrium pairs for free 1-person games as well as for free 1-person games. Our results extend and improve several well-known and recent results.