General Topology-I

In this paper, we introduce a new concept of α – ψ -contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.

Fixed point theorems for α–ψ-contractive type mappings

Elementary Fixed Point Theorems * Theorem of Borsuk and Topological Transversality * Homology and Fixed Points * Leray-Schauder Degree and Fixed Point Index * The Lefschetz-Hopf Theory * Selected Topics * Index

Fixed Point Theory

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Metric Spaces Of Non Positive Curvature

Some Results on Fixed Points

We establish coincidence fixed point and common fixed point theorems for mappings satisfying ( ψ , φ ) -weakly contractive condition in an ordered complete metric space. Some applications of our obtained results are given.

Fixed point results for mappings satisfying (ψ,φ)-weakly contractive condition in partially ordered metric spaces

The purpose of this paper is to establish a coupled coincidence point for a pair of commuting mappings in partially ordered complete metric spaces. We also present a result on the existence and uniqueness of coupled common fixed points. An example is given to support the usability of our results.

Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces

Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces

We establish a fixed point theorem for nonlinear contraction in a complete partial metric space. Our result generalizes the Banach type fixed point theorem in a partial metric space in the sense of Matthews. c ©2012 NGA. All rights reserved.

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Hemant Kumar Nashine

Papers

Fixed point results for mappings satisfying (ψ,φ)-weakly contractive condition in partially ordered metric spaces

Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces

Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces

A generalization of Banachs contraction principle for nonlinear contraction in a partial metric space

Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces