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A note on the weak convergence of a sequence of successive approximations

Kalinde A., Mishra S., Singh S.

Demonstratio Mathematica

2006

Vol. 39, nr 3

619-624

In this paper we discuss the weak convergence of the sequence of successive approximations for a generalized para-nonexpansive mapping in a reflexive Banach space that satisfies Opial's condition.

Common fixed point theorems with applications to nonlinear integral equations

Pathak H., Mishra S., Kalinde A.

Demonstratio Mathematica

1999

Vol. 32, nr 3

547-564

Various definitions of compatible maps are characterized and compared in terms of continuity of maps, fixed points and certain limits. Common fixed point theorems for a new class of compatible maps on complete metric spaces are proved. Subsequently, the main result is applied to prove the existence of solutions of two systems of nonlinear integral equation.