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On Majorization for Matrices

Khan, M. AdilLatif, NaveedPecaric, J.Peric, I. — 2013

Mathematica Balkanica New Series

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities...

An existence theorem for extended mildly nonlinear complementarity problem in semi-inner product spaces

M. S. Khan — 1995

Commentationes Mathematicae Universitatis Carolinae

We prove a result for the existence and uniqueness of the solution for a class of mildly nonlinear complementarity problem in a uniformly convex and strongly smooth Banach space equipped with a semi-inner product. We also get an extension of a nonlinear complementarity problem over an infinite dimensional space. Our last results deal with the existence of a solution of mildly nonlinear complementarity problem in a reflexive Banach space.

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.

On the convergence of the Ishikawa iterates to a common fixed point of two mappings

Ljubomir B. ĆirićJeong Sheok UmeM. S. Khan — 2003

Archivum Mathematicum

Let C be a convex subset of a complete convex metric space X , and S and T be two selfmappings on C . In this paper it is shown that if the sequence of Ishikawa iterations associated with S and T converges, then its limit point is the common fixed point of S and T . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].

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