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Some stability results in complete metric space

Memudu Olaposi Olatinwo (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we obtain some stability results for the Picard iteration process for one and two metrics in complete metric space by using different contractive definitions which are more general than those of Berinde [Berinde, V.: On the stability of some fixed point procedures. Bul. Stiint. Univ. Baia Mare, Ser. B, Matematica–Informatica 18, 1 (2002), 7–14.], Imoru and Olatinwo [Imoru, C. O., Olatinwo, M. O.: On the stability of Picard and Mann iteration processes. Carpathian J. Math. 19, 2 (2003),...

Some stability theorems for some iteration processes

C. O. Imoru, Memudu Olaposi Olatinwo (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we obtain some stability results for Picard and Mann iteration processes in metric space and normed linear space respectively, using two different contractive definitions which are more general than those of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1, 2], Imoru and Olatinwo [5] and Imoru et al [6].Our results are generalizations of some results of Harder and Hicks [4], Rhoades [10, 11], Osilike [8], Osilike and Udomene [9], Berinde [1,...

Some surjectivity theorems with applications

H. K. Pathak, S. 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...

Sur un problème parabolique-elliptique

Philippe Benilan, Petra Wittbold (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like ( v - 1 ) t + = v x x + F ( v ) x where the function F : is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.

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