Recent Developments of Cone metric spaces over Banach algebra

ISBN-13: 9786204202037 / Angielski / Miękka / 132 str.

Jerolina Fernandez; Neeraj Malviya

Opis

The book comprises of seven chapters.Chapter 1 we present some preliminaries that will be needed in the sequel.Chapter 2 we introduce the notion of partial cone metric spaces over Banach algebra and prove fixed point results.Chapter 3 we propose a generalization called partial cone b-metric spaces over Banach algebra, replacing Banach spaces by Banach algebra.In Chapter 4 we define J-cone metric spaces over Banach algebra. We study the topological and structural properties of the new space and derive some fixed point theorems.In Chapter 5 we establish some coupled fixed point results for generalized Lipschitz mappings verifying in J-cone metric space over Banach algebra.Chapter 6 we introduce the concept of cone b_2-metric space over Banach algebra. Next, we define generalized Lipschitz and expansive maps in the new structure and establish the existence and uniqueness of fixed points for such mappings.In Chapter 7 we devote our study to introduce the structure of N-cone metric space over Banach algebra. We define generalized Lipschitz mapping and prove some fixed point results for such mappings in the new framework.

O autorze

Fernandez, JerolinaDr. Jerolina Fernandez is an Assistant Professor at The Bhopal School of Social Sciences, Bhopal, M. P., India. She has obtained her Ph.D. from Barkatullah University, India. Dr. Neeraj Malviya obtained his Ph.D. from Barkatullah University, Bhopal and is an Assistant Professor in Department of Mathematics, Government College Timarni, Harda, India.