Jatinderdeep Kaur

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.

Fixed point theorems for ( ξ , α ) -expansive mappings in complete metric spaces

In this paper, we introduce a new, simple and unified approach to the theory of expansive mappings. We present a new category of expansive mappings called (ξ,α)-expansive mappings and study various fixed point theorems for such mappings in complete metric spaces. Further, we shall use these theorems to derive coupled fixed point theorems in complete metric spaces. Our new notion complements the concept of α-ψ-contractive type mappings introduced recently by Samet et al. (Nonlinear Anal. 2011, doi:10.1016/j.na.2011.10.014). The presented theorems extend, generalize and improve many existing results in the literature. Some comparative examples are constructed which illustrate our results in comparison to some of the existing ones in literature.

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.

L1-convergence of modified complex trigonometric sums

In this paper, we shall study the L1-convergence of complex form of modified cosine and sine sums as a02+ ∑ k = 1n ∑ j = knΔ(ajcosjx) and ∑ k = 1n ∑ j = knΔ(ajsinjx). Also, using the complex form of above modified trigonometric sums, we shall obtain a new necessary and sufficient condition for the L1-convergence of Fourier series.