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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.

Growing a class of fractals based on combination of classical fractals and recursive mathematical series in L-systems

Bisoi A. K., Mishra S. N., Mishra J.

Machine Graphics and Vision

2004

Vol. 13, No. 3

275-288

L-systems can be used to generate fractals. In this paper L-systems with a standard turtle alphabet are combined with L-systems which emulate simple number sequences. The combination of two such L-systems is achieved by concatenating their axioms as well as merging their rule sets. This can happen in several ways, depending in part on the sequence in which axioms and right-hand sides of rules are concatenated. The purpose of this paper is to combine these two applications of L-systems to generate novel fractals. A turtle interpretation is applied to the yield of the generated hybrid L-systems resulting in new fractal images.

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.