Satvinder Singh Bhatia

Generalized (ξ,α)-expansive mappings and related fixed-point theorems

In this paper, we introduce a new class of expansive mappings called generalized (ξ,α)-expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results.MSC:46T99, 54H25, 47H10, 54E50.

Convergence of modified complex trigonometric sums in the metric space L

We study the L1-convergence of new modified complex trigonometric sum and obtain a new necessary and sufficient condition for the L1-convergence of Fourier series.

Development of a standard text and speech corpus for the Punjabi language

In this paper, a new text and speech corpus in the Punjabi language has been developed. The Punjabi language is a modern Indo-Aryan language. The Punjabi language has been ranked amongst the top spoken languages of the world. Over the years, this ranking has varied between 10 and 18. Any research work on the Punjabi language, therefore, assumes an international significance. The Punjabi language is the native language of the Punjab state in two countries: East Punjab in India, and West Punjab in Pakistan. There are many dialects of the Punjabi language and two different scripts in both countries. It will be an enormous task to design a new text or speech corpus that can completely describe all dialects in both scripts. This work, therefore, concentrates only on one dialect of the Punjabi language: the Malwai dialect. This paper describes at least 20 unique features of the newly designed corpus.

Numerical solution of stochastic partial differential difference equation arising in reliability engineering

In this paper, a numerical method is proposed to solve the transient state of Markovian system of equations. Such equations appear in the field of reliability engineering for systems having variable failure and repair rates. Generally, steady state behaviour of the system model is studied due to some constraint on obtaining transient state solution. The proposed method helps to determine the probability values, by utilizing finite difference scheme iteratively in conjunction with the results of integral appearing in stochastic differential difference equation obtained using supplementary variable technique. This method also uses the Lagranges method to interpolate the missing value of repair rates of the system wherever required in computation. Results thus obtained are found to be efficient for studying the transient state behaviour of the system.

Nonexistence of Totally Contact Umbilical Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

We study totally contact umbilical slant lightlike submanifolds of indefinite cosymplectic manifolds. We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds in indefinite cosymplectic manifolds other than totally contact geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite cosymplectic space forms. Finally we give characterization theorems on minimal slant lightlike submanifolds.

The axioms of indefinite hemi-slant planes and spheres

We define the axiom of indefinite hemi-slant 3-planes and 3-spheres for an indefinite almost Hermitian manifold with lightlike submanifolds. We prove that if an indefinite Kaehler manifold satisfies the axioms of indefinite hemi-slant 3-planes and 3-spheres for some slant angle θ ∈ (0, π/2) then it is an indefinite complex space form.

Common Fixed Points of Expansive Mappings in Generalized Metric Spaces

In this paper, we establish a common fixed point theorem for expansive mappings by using the concept of weakcompatibility in the setting of G -metric spaces. This result generalizes the result of Ahmed [2] from 2-metric spaces toG -metric spaces by removing the condition of sequential continuity of the mappings. Further, we generalize andextend the theorem of Şahin and Telci [20] to G -metric spaces and thereby extending the theorem of Wang et al. [23]for a pair of mappings to G -metric spaces. Some comparative examples are constructed which illustrate the obtainedresults.