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Some surjectivity theorems with applications

H. K. PathakS. N. Mishra — 2013

Archivum Mathematicum

In this paper a new class of mappings, known as locally λ -strongly φ -accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ -accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ -strongly φ -accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion...

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

H. K. PathakM. S. Khan — 1999

Czechoslovak Mathematical Journal

In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

H. K. PathakShin Min KangYeol Je Cho — 1998

Czechoslovak Mathematical Journal

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.

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