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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Penelitian Pendidikan IPA (JPPIPA) Hilbert Journal of Mathematical Analysis
Ratno Bagus Edy Wibowo
Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Control & Systems Engineering Education Engineering Materials Science & Nanotechnology Mathematics Physics

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Legendre-Fenchel duality in m-convexity Wibowo, Ratno Bagus Edy; Marjono; Pramana, Eko Dedi
Hilbert Journal of Mathematical Analysis Vol. 2 No. 2 (2024): Hilbert J. Math. Anal.
Publisher : KOMUNITAS Analisis Matematika INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62918/hjma.v2i2.23

Abstract

The Legendre-Fenchel transform, which maps a function to its convex conjugate, provides a dual perspective that is fundamental in understanding optimization problems. In this work, we show that m-convex function in n-dimensional normed spaces can be viewed as the Legendre-Fenchel dual problem. By constructing an epi-graph of m-convexity in n-dimensional normed spaces, we obtained some properties including the Legendre transform. Particularly, we prove this for certain convex functions.
Jensen m-Convexity on Set-Valued Function Pramana, Eko Dedi; Wibowo, Ratno Bagus Edy; Muslikh, Mohamad
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.26901

Abstract

This paper discusses the class of Jensen m-convex functions and their properties, leading to enhancements of these functions and Jensen's inequalities for set-valued functions. It provides several characterizations and explores various algebraic properties. Additionally, it introduces a discrete Jensen-type inclusion.
Evaluation of Sustainable Tourism of Pacal Reservoir Based on Environment, Economic and Social Perspectives in Bojonegoro Regency Anita, Yuli; Semedi, Bambang; Wibowo, Ratno Bagus Edy; Hidayati, Bunga
Jurnal Penelitian Pendidikan IPA Vol 11 No 1 (2025): January
Publisher : Postgraduate, University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jppipa.v11i1.10327

Abstract

Pacal Reservoir has a function to irrigate agriculture in the Bojonegoro Regency area. Pacal Reservoir also has beautiful natural potential so that it is used as a mainstay tourism object of Bojonegoro Regency. The existence of the reservoir that has been for 90 years, makes the pacal reservoir experience several problems. The purpose of this study is to analyze pacal reservoir tourism into sustainable tourism. The method used is qualitative descriptive. The analysis used is a SWOT analysis. The results of the SWOT analysis are at the coordinate point (0.37; 0.28) where the coordinate point is in quadrant I. So that pacal reservoir tourism has opportunities and strengths, namely in that position is the most advantageous situation. Based on this study, it can be concluded that the results of the SWOT matrix produce several strategies when viewed in terms of environmental, social and economic tourism of the pacal reservoir. The result of the SWOT coordinate point is in quadrant I. Position in quadrant I means having opportunity and strength. The strategy that must be taken in conditions like this is to support an aggressive growth-oriented strategy by utilizing existing opportunities and strengths possessed.
Co-Authors Anita, Yuli Bambang Semedi Bunga Hidayati Marjono Mohamad Muslikh Pramana, Eko Dedi