Ljubomir Ćirić

Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces

A concept of -monotone mapping is introduced, and some fixed and common fixed point theorems for -non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. (2008).

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.

Common fixed points of generalized contractions on partial metric spaces and an application

Abstract In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778–2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.

Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces

In this article, a new concept of mixed monotone-generalized contraction in partially ordered probabilistic metric spaces is introduced, and some coupled coincidence and coupled fixed point theorems are proved. The theorems Presented are an extension of many existing results in the literature and include several recent developments.Mathematics Subject Classification: Primary 54H25; Secondary 47H10.

IMPLICIT MANN FIXED POINT ITERATIONS FOR PSEUDO-CONTRACTIVE MAPPINGS

Abstract Let K be a compact convex subset of a real Hilbert space H and T : K → K a continuous hemi-contractive map. Let { a n } , { b n } and { c n } be real sequences in [0, 1] such that a n + b n + c n = 1 , and { u n } and { v n } be sequences in K . In this paper we prove that, if { b n } , { c n } and { v n } satisfy some appropriate conditions, then for arbitrary x 0 ∈ K , the sequence { x n } defined iteratively by x n = a n x n − 1 + b n T v n + c n u n ; n ≥ 1 , converges strongly to a fixed point of T .

Coupled coincidence and common fixed point theorems for hybrid pair of mappings

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two single valued maps. In this article, we extend these concepts to multi-valued mappings and obtain coupled coincidence points and common coupled fixed point theorems involving hybrid pair of single valued and multi-valued maps satisfying generalized contractive conditions in the frame work of a complete metric space. Two examples are presented to support our results.2000 Mathematics Subject Classification: 47H10; 47H04; 47H07.

Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications

We derive some new coupled fixed point theorems for nonlinear contractive maps that satisfied a generalized Mizoguchi-Takahashis condition in the setting of ordered metric spaces. Presented theorems extends and generalize many well-known results in the literature. As an application, we give an existence and uniqueness theorem for the solution to a two-point boundary value problem.2000 Mathematics Subject Classification: 54H25; 47H10.

On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings

Abstract For a Lipschitz strongly accretive map considered by Chidume in [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint No. IC2000098; C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear analysis and applications: to V. Lakshmikantam on his 80th birthday, vols. 1 and 2, Kluwer Acad. Publ., Dordrecht, 2003, pp. 383–429], it is known that a classical Picard-type iteration process converges strongly to a zero of the operator. He also proved that the rate of convergence, in this case, is at least as fast as a geometric progression. In this paper we study the Mann implicit iteration sequence for strongly accretive and strongly pseudo-contractive mappings. We showed that this implicit scheme gives better convergence rate estimate. Presented results improve the corresponding results of [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint No. IC2000098; C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear analysis and applications: to V. Lakshmikantam on his 80th birthday, vols. 1 and 2, Kluwer Acad. Publ., Dordrecht, 2003, pp. 383–429; L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Am. Math. Soc. 125 (2) (1997) 1363–1366; W.R. Sastry, G.V.R. Babu, Approximation of fixed points of strictly pseudo-contractive mappings on arbitrary closed, convex sets in a Banach space, Proc. Amer. Math. Soc. 128 (2000) 2907–2909; Y. Song, R. Chen, Viscosity approximative methods to Cesaro means for non-expansive mappings, Appl. Math. Comput. 186 (2) (2007) 1120–1128].

Fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces

In this article, we introduce the concept of a w-cone distance on topological vector space (tvs)-cone metric spaces and prove various fixed point theorems for w-cone distance contraction mappings in tvs-cone metric spaces. The techniques of the proof of our theorems are more complex then in the corresponding previously published articles, since a new technique was necessary for the considered class of mappings. Presented fixed point theorems generalize results of Suzuki and Takahashi, Abbas and Rhoades, Pathak and Shahzad, Raja and Veazpour, Hicks and Rhoades and several other results existing in the literature.Mathematics subject classification (2010): 47H10; 54H25.

Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics

Abstract In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived.