Article
Mathematics, Applied
Huseyin Bor
Summary: In this paper, we present two main theorems regarding absolute weighted arithmetic mean summability factors of infinite series and trigonometric Fourier series. These theorems have been generalized for a general summability method, and new and known results have also been obtained for certain absolute summability methods.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Hueseyin Bor
Summary: The paper focuses on two main theorems dealing with the |N over line, p(n)|(k) summability factors of infinite series and trigonometric Fourier series, and generalizes them for the |N over line, p(n); theta(n)|(k) summability methods. It also obtains some new and known results for certain absolute summability methods.
BULLETIN DES SCIENCES MATHEMATIQUES
(2022)
Article
Mathematics, Applied
Huseyin Bor
Summary: This paper improves a known theorem of Mazhar under weaker conditions and applies it to the trigonometric Fourier series, obtaining some new results. Published by Elsevier Masson SAS.
BULLETIN DES SCIENCES MATHEMATIQUES
(2021)
Article
Mathematics, Applied
Sebnem Yildiz
Summary: The study by Bor (2021) proved two main theorems on absolute Riesz summability factors, which were then generalized to a specific summability method in this paper. The results were published by Elsevier Masson SAS in 2021.
BULLETIN DES SCIENCES MATHEMATIQUES
(2021)
Article
Mathematics
Josip Pecaric, Jurica Peric, Sanja Varosanec
Summary: We provide a refinement of the converse Holder inequality for functionals by using an interpolation result for Jensen's inequality. In addition, we improve the converse of the Beckenbach inequality. We also consider the converse Minkowski inequality for functionals and give refinements of it, along with applications on integral mixed means.
Article
Mathematics, Interdisciplinary Applications
Shanhe Wu, Muhammad Samraiz, Sajid Iqbal, Gauhar Rahman
Summary: In this paper, a new class of Hardy-type inequalities involving fractional calculus operators is studied. Hardy-type inequalities are derived for the variant of Riemann-Liouville fractional calculus operators and k-Hilfer fractional derivative operator. The obtained inequalities involving fractional operators are more general as compared to some existing results in the literature.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Sebnem Yildiz
Summary: This matrix generalization result deals with weighted mean summability of infinite series using a new general class of power increasing sequences obtained by Sulaiman [9], and includes new and known results related to basic summability methods.
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS
(2021)
Article
Mathematics, Applied
Ying Wu, Feng Qi
Summary: In this paper, the authors demonstrate the errors in the proofs of Theorems 1 and 2 in a previous paper by constructing a counterexample and utilizing Minkowski's inequality. They also present a new integral inequality of the Hermite-Hadamard type for convex functions using an integral identity and Holder's integral inequality.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Huseyin Bor
Summary: In this paper, we have proved a general theorem on the phi-summability factors of infinite series and obtained new and known results related to different special summability methods.
JOURNAL OF APPLIED MATHEMATICS & INFORMATICS
(2022)
Article
Mathematics
Slavko Simic, Vesna Todorcevic
Summary: This article provides sharp two-sided bounds for the generalized Jensen functional J(n)(f,g,h;p,x) and exact bounds for the generalized quasi-arithmetic mean A(n)(h;p,x) by assuming convexity/concavity of the generating function h. It also determines exact bounds for the generalized power means in terms from the class of Stolarsky means, leading to sharp converses of Holder's inequality.
Article
Mathematics
Hikmet Seyhan Ozarslan, Ahmet Karakas
Summary: This paper studies the absolute matrix summability of an infinite series and generalizes a known theorem dealing with summability factors of an infinite series. The new theorem also includes some results.
TBILISI MATHEMATICAL JOURNAL
(2021)
Article
Mathematics, Applied
S. H. Saker, J. Alzabut, D. O'Regan, R. P. Agarwal
Summary: This paper proves the self-improving property of the weighted Gehring class in non-homogeneous spaces, obtaining sharp bounds of exponents and applying it to the self-improving property of the Muckenhoupt class. By utilizing rearrangement of functions and Jensen inequality, the results cover non-monotonic functions and provide a higher integrability theorem. Furthermore, solutions of partial differential equations can be solved in an extended space using this self-improving property, reflecting a different approach to inequalities of Hardy type.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
S. H. Saker, R. R. Mahmoud, K. R. Abdo
Summary: The characterization of non-negative weight pairs (u, v) satisfying Hardy-type dynamic inequalities on time scale T is achieved in the spaces Lpv(T) and Lqu(T ). Two different scenarios of exponent values p and q are considered, complementing the classical (p, p) results and their generalizations. Continuous and discrete results for the quantum space $N0 for $ > 1 are provided, as well as applications related to the results obtained by Anderson, Heinig, Kufner, Flett, and Saker.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Huseyin Bor
Summary: This paper proved a general theorem regarding the phi -| C, alpha, beta |(k) summability factors of infinite series, and further derived some new and known results.
QUAESTIONES MATHEMATICAE
(2021)
Article
Mathematics
Rabia Bibi
Summary: This paper obtains refinement of the Holder's inequality and its related inequalities, including integral Minkowski's inequality and some Hardy type inequalities on time scales.
MATHEMATICAL INEQUALITIES & APPLICATIONS
(2022)
