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Remarks on occasionally weakly compatible maps versus occasionally weakly compatible maps

Deepmala, Pathak H. K.

Demonstratio Mathematica

2014

Vol. 47, nr 3

695--703

In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some additional conditions on their results.

Some weakly contractive mapping theorems in partially ordered spaces and applications

Rhoades B. E., Pathak H. K., Mishra S. N.

Demonstratio Mathematica

2012

Vol. 45, nr 3

621-636

The purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly (…)-contractive mappings, in a complete metric space endowed with a partial ordering. Subsequently, we apply our main results to obtain a solution of a first order periodic problem and study the possibility of optimally controlling the solutions of ordinary differential equations via dynamic programming.

Some Gregus type common fixed point theorems with applications

Pathak H. K., Mishra S. N., Kalinde A. K.

Demonstratio Mathematica

2003

Vol. 36, nr 2

413--426

In this paper a Gregus type common fixed point theorem for coincidently commuting mappings is proved and utilized to obtain the iterative solution of certain variational inequalities.