Refinements of two fractional versions of Hadamard inequalities for Caputo fractional derivatives and related results
OMS-Vol. 5 (2021), Issue 1, pp. 1 – 10 Open Access Full-Text PDF
Ghulam Farid, Atiq Ur Rehman, Sidra Bibi, Yu-Ming Chu
Abstract: The aim of this paper is to study the fractional Hadamard inequalities for Caputo fractional derivatives of strongly convex functions. We obtain refinements of two known fractional versions of the Hadamard inequality for convex functions. By applying identities for Caputo fractional derivatives we get refinements of error bounds of these inequalities. The given results simultaneously provide refinements as well as generalizations of already known inequalities.
Some basic properties of Sombor indices
ODAM-Vol. 4 (2021), Issue 1, pp. 1 – 3 Open Access Full-Text PDF
Ivan Gutman
Abstract: The recently introduced class of vertex-degree-based molecular structure descriptors, called Sombor indices (\(SO\)), are examined and a few of their basic properties established. Simple lower and upper bounds for \(SO\) are determined. It is shown that any vertex–degree–based descriptor can be viewed as a special case of a Sombor-type index.
On Adomian decomposition method for solving nonlinear ordinary differential equations of variable coefficients
OMS-Vol. 4 (2020), Issue 1, pp. 476 – 484 Open Access Full-Text PDF
AbdulAzeez Kayode Jimoh, Aolat Olabisi Oyedeji
Abstract: This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.
Some applications of second-order differential subordination for a class of analytic function defined by the lambda operator
OMA-Vol. 4 (2020), Issue 2, pp. 170 – 177 Open Access Full-Text PDF
B. Venkateswarlu, P. Thirupathi Reddy, S. Sridevi, Sujatha
Abstract: In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.
Best proximity point of modified Suzuki-Edelstein-Geraghty type proximal contractions
EASL-Vol. 3 (2020), Issue 4, pp. 94 – 104 Open Access Full-Text PDF
Leta Bekere Kumssa
Abstract: In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.
On properties of inner product type integral transformers
OMA-Vol. 4 (2020), Issue 2, pp. 160 – 169 Open Access Full-Text PDF
Benard Okelo
Abstract: In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.
