Paper's Title:

Fractional class of analytic functions Defined Using q-Differential Operator

Author(s):

K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan

Department of Mathematics and Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
E-mail: kr_karthikeyan1979@yahoo.com

College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
E-mail: musthafa.ibrahim@gmail.com

Department of Mathematics, Presidency College (Autonomous),
Chennai-600005, Tamilnadu,
India.
 

Abstract:

We define a q-differential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving q-differential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.

Paper's Title:

Characterization of Caristi Type Mapping Through its Absolute Derivative

Author(s):

M. Muslikh¹, A. Kilicman^2,3, S. H. Sapar⁴ and N. Bacho⁵

¹Department of Mathematics,
University of Brawijaya,
Malang 65143, East Java,
Indonesia.
E-mail: mslk@ub.ac.id

²Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: akilic@upm.edu.my

³Department of Electrical and Electronic Engineering,
Istanbul Gelisim University,
Avcilar, Istanbul,
Turkey

⁴Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: sitihas@upm.edu.my

⁵Department of Mathematics,
Universiti Putra Malaysia,
43400 UPM, Serdang, Selangor,
Malaysia
E-mail: norfifah@upm.edu.my

Abstract:

The purpose of this article to characterize the Caristi type mapping by the absolute derivative. The equivalences of the Caristi mapping with contraction mapping is discussed too. In addition, it was shown that the contraction mapping can be tested through its absolute derivative.

Paper's Title:

Some criteria for Subspace-hypercyclicity of C₀-semigroups

Author(s):

Mansooreh Moosapoor

Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: m.mosapour@cfu.ac.ir
mosapor110@gmail.com
 

Abstract:

We research subspace-hypercyclic C₀-semigroups in this paper. We present various types of subspace-hypercyclicity criteria for C₀-semigroups. Some of them are stronger than the criteria introduced before. Also, we state that if a C₀-semigroup (T_t}_{t≥ 0} satisfies in any of them, then (T_t⊕T_t}_{t≥ 0} is subspace-hypercyclic.

Paper's Title:

Some Double λ-Convergent Sequence Spaces Over n-Normed Spaces

Author(s):

Kuldip Raj, Renu Anand and Seema Jamwal

School of Mathematics,
Shri Mata Vaishno Devi University Katra-182320,
Jammu and Kashmir,
India.

E-mail: kuldipraj68@gmail.com,  renuanand71@gmail.com, seemajamwal8@gmail.com

Abstract:

In this paper we introduce some double generalized λ-convergent sequence spaces over n-normed spaces defined by Musielak-Orlicz function M = (M_k,l). We also made an attempt to study some topological and algebraic properties of these sequence spaces.

Paper's Title:

On Subspace-Supercyclic Operators

Author(s):

Mansooreh Moosapoor

Assistant Professor,
Department of Mathematics,
Farhangian University, Tehran,
Iran.
E-mail: mosapor110@gmail.com m.mosapour@cfu.ac.ir

Abstract:

In this paper, we prove that supercyclic operators are subspace-supercyclic and by this we give a positive answer to a question posed in ( L. Zhang, Z. H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal., 6 (2015), pp. 60--68). We give examples of subspace-supercyclic operators that are not subspace-hypercyclic. We state that if T is an invertible supercyclic operator then Tⁿ and T^-n is subspace-supercyclic for any positive integer n. We give two subspace-supercyclicity criteria. Surprisingly, we show that subspace-supercyclic operators exist on finite-dimensional spaces.

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